ATM More Fun with Slevogt Collimation

[Aplanatic@aol.com]

As you may recall, I recently finished a Slevogt camera (concentric Schmidt
Cassegrain) and have even taken a nice picture or two with it.  An interesting
problem that I have been facing is the mechanical and optical collimation of
the system.

The camera uses a medium format film frame having a maximum off-axis distance
of 1.5".  The fast f/ratio of the camera (4.5) dictates that all areas of the
film plane be within 3 mils of the focal plane to take maximum advantage of
the fine resolution of the optics.  Thus, the film plane must be aligned to
the focal plane to better than 2 milliradians.  A better way of saying this
is:  The vector normal to the film plane must be within 2 milliradians of the
vector normal to the focal plane.

What determines the focal plane in a concentric Schmidt Cass having spherical
primary and secondary mirrors?  Answer:  The vector normal to the focal plane
passes through the center of curvature (CoC) of both mirrors, dictated by the
spherical symmetry of the system.  The corrector plate has no first order
effect on the focal plane, but its center must lie on the line joining the two
CoCs for good collimation.  That's the whole story as Bratislav correctly
stated.

Now, how does one co-linearize the film plane's normal vector, primary CoC,
secondary CoC and the corrector plate center?  Can a laser collimator be used?
What are the errors involved?

We must first review the geometry of the CSCT.  The primary has a radius of
curvature (RoC) of 44 inches.  The secondary has an RoC of 43 inches and lies
12" from the primary.  Thus, the CoC of the primary and the CoC of the
secondary are 11" from each other.  The corrector plate is 50" from the
primary and is supported by an open truss tube structure.

The collimation procedure using a laser is as follows:

1) The laser beam is squared to the film plane.  This is accomplished by
rotating the off-axis guider (OAG) (which has been machined square to the film
plane) while watching the laser spot on a wall some distance away.  The diode
in the collimator is adjusted until the spot does not move during rotation of
the OAG.  In practice, I can adjust the laser diode to about 0.5 milliradians
with this technique.  I can't do much better than this because of the
cumbersome method of adjustment used in the collimator, and because the diode
seems to move over time due to plastic flow or stress relief inside the
collimator head.

2) A white reflective screen is placed at the CoC of the primary mirror,
supported by the truss tube assembly.  The laser spot is scattered by this
surface and this scattered light is reflected by the primary and refocused
onto the white screen.  Of course, the secondary mirror has been removed for
this operation.  Now, the primary mirror cell is adjusted so that the
reflected image of the spot coincides with the spot itself.  In practice,
because of the large diameter of the spot produced by the laser diode, there
will be some error in collimation from this step.  I believe that I can
estimate the spot's centroid to about 1/5 of its diameter.  Since the spot
diameter is about 0.1" at the screen location, the possible error in locating
the CoC of the primary is about 20 mils.

3) Finally, the secondary is re-installed and adjusted until the laser spot
returns to its origin.  To facilitate this, a piece of aluminum foil with a 10
mil pinhole was glued to the face of the collimator so that the centroid of
the returned beam could more easily be determined.  Because of beam divergence
in the laser diode, and because of the defocusing effect of the convex
secondary, the returned spot is about 0.2" in diameter.  Again assuming that I
can reliably estimate the centroid to 1/5 of its diameter, this alignment will
have a possible error of 40 mils in the placement of the CoC of the secondary.
(There is some trivial geometry involved in this estimation.  The collimator
is about 19" from the secondary.)

So, the primary CoC can be off by as much as 20 mils, the secondary CoC can be
off by as much as 40 mils and the line joining them is 11" long.  This
translates into a possible worst case error of about 6 milliradians.  This is
a factor of three larger than acceptable.

What can be done?  Is the laser diode method of collimation doomed to fail
some or even most of the time?  Can the laser beam divergence be reduced by
the use of pinholes and lenses so that a better estimate of the spot's
centroid can be made?  What other options are there for film plane
collimation?

For those of you that made it all the way to the end of this discussion, I
admire your patience and attention span.

Thanks,

Dave Rowe
Torrance, CA